How Correlations Influence Lasso Prediction
By Mohamed Hebiri, Johannes Lederer. 2012
107 citations recorded by the source corpus.
We study how correlations in the design matrix influence Lasso prediction. First, we argue that the higher the correlations, the smaller the optimal tuning parameter. This implies in particular that the standard tuning parameters, that do not depend on the design matrix, are not favorable. Furthermore, we argue that Lasso prediction works well for any degree of correlations if suitable tuning parameters are chosen. We study these two subjects theoretically as well as with simulations.
Subfields: Artificial Intelligence, Finance, Statistics and Probability
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Citations in the corpus
- Sparse Partially Linear Additive Models (2014, background): “Such bounds have been improved for the lasso by careful incorporation of the design matrix (Hebiri and Lederer 2013), and we speculate that similar improvement could be developed here.”
- Non-negative least squares for high-dimensional linear models: consistency and sparse recovery without regularization (2012, background): “In [25, 53], improvements of the slow rate bound are derived.”
- Probabilistic forecasting in day-ahead electricity markets: Simulating peak and off-peak prices (2018, methodology): “If α = 1 the estimation method is equivalent to the lasso penalty developed by Tibshirani (1996), and when α = 0 it is equivalent to the ridge penalty first introduced by Hoerl and Kennard (1970). The lasso estimator has the property of sparsity, which means that for certain values of λ the resultin”